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Nonlinear Multiregressions Based On Choquet Integral For Data With Both Numerical And Categorical Attributes., Jin Hui
Student Work
Based on generalized Choquet integrals with respect to signed fuzzy measures, a model of nonlinear multiregression that can catch the interaction among predictive attributes toward the objective attribute can be established. In this model, some predictive attributes are numerical while the others are categorical. A numericalization technique is adopted to project each state of a categorical attribute that has more than two states to a multi-dimensional space optimally through a genetic algorithm, in which some regression coefficients are determined from data. To reduce the complexity of the genetic algorithm, the other regression coefficients such as the values of the signed …
Elementary Cellular Automata, Fractal Dimensions And Mutual Information., Naomi Kochi
Elementary Cellular Automata, Fractal Dimensions And Mutual Information., Naomi Kochi
Student Work
We explore a quantitative description of Wolfram's classification of elementary cellular automata based on fractal dimensions. We find the· fractal dimension to be a global measure in classifying elementary cellular automata independent of initial conditions. On the other hand, the results of our analysis of rules in Class 3 numerically confirm the existence of a wide range of dynamics among rules in Class 3. The main reason for this is due to the fact that the rules with the Sierpinski structure in Class 3 have the capacity to behave like rules in Class 2 depending on their initial conditions. Furthermore, …
Solving Nonlinear Optimization Problems That Have A Nondifferentiable Objective Function By Using A Pseudo Gradient Search., Marie Louise Spilde
Solving Nonlinear Optimization Problems That Have A Nondifferentiable Objective Function By Using A Pseudo Gradient Search., Marie Louise Spilde
Student Work
The gradient search fails in an optimization problem where the objective function is not differentiable--such as nonlinear multiregressions based on generalized Choquet integrals. In cases such as this, we may replace the gradient search with a pseudo gradient search to determine the optimal search direction. The pseudo gradient can be obtained algorithmically from a data set containing the objective attribute and relevant arguments of the objective function. The algorithm for the pseudo gradient search is based on a neural network model which uses statistical techniques such as root mean square error to determine the optimal search direction and the optimal …
Noise Reduction In Time Series Data From Dynamical Systems., Richard Lyman Warr
Noise Reduction In Time Series Data From Dynamical Systems., Richard Lyman Warr
Student Work
Introduction: The objective of this thesis is to determine if the amount of noise in the observed time series data has affected the outcome of the chaotic descriptors. To thoroughly analyzed this problem I will first introduce how the data was obtained, next how to find the chaotic descriptors, and then discuss and apply noise reduction techniques.